This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A165217 #19 Jun 25 2023 20:50:16 %S A165217 6,25,50,145,224,497,630,1281,1606,2761,3302,5265,5940,9185,10472, %T A165217 14977,16834,23161,25284,34321,37720,49105,53500,68225,73278,92457, %U A165217 99470,122641,131316,159681,169158,204545,217210,258265,273282,321937,338208,396721,417380,483841,507830 %N A165217 Count of interior bounded regions in a regular 2n-sided polygon dissected by all diagonals parallel to sides. %C A165217 The rule is: get a regular polygon with at least 6 sides and an even number of sides (hexagon, octagon, etc.) and pick a point, then pick the point directly clockwise it, draw a line then draw lines parallel to it going through the other points. Then do the same with all the other points. a(n) is the count of interior bounded regions. %C A165217 Please email me if you can find a pattern! %H A165217 R. J. Mathar, <a href="https://arxiv.org/abs/0911.3434">Tile Count in the Interior of Regular 2n-Gons Dissected by Diagonals Parallel to Sides</a>, arxiv:0911.3434 [math.CO], 2009. %H A165217 <a href="/index/Pol#Poonen">Index to sequences on drawing diagonals in regular polygons</a> %F A165217 Conjecture: a(2n) = (2*n-1)*(4*n^3-4*n^2+6*n-3)/3. - Thomas Young (tyoung(AT)district16.org), Dec 23 2018 %Y A165217 Cf. A003454, A320422 %K A165217 nonn %O A165217 3,1 %A A165217 Chintan (timtamboy63(AT)gmail.com), Sep 08 2009 %E A165217 a(6)-a(8) corrected and a(9)-a(10) added by _R. J. Mathar_, Oct 09 2009 %E A165217 a(11)-a(22) from _R. J. Mathar_, Nov 19 2009 %E A165217 Typo in a(14) corrected by Thomas Young (tyoung(AT)district16.org), Dec 23 2018 %E A165217 a(23)-a(43) from _Christopher Scussel_, Jun 25 2023